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avatar+386 

 

We have the following:

 

Triangle with sides "a" "b" "c"  (c being the hypotenuse)

 

hypotenuse = c = 15cm

 

there is 3 cm of difference between a and b

 

so let's say

 

a = b - 3

 

b = a - 3

 

Pythagorean theorem: a^2 + b^2 = c^2

 

replace:

 

a^2 + (a-3)^2 = 15

 

Where do you go from there to find a and b ?

 Dec 18, 2016
 #1
avatar+129852 
0

Note   ......we can't  have that

 

a = b −3    and   b  = a − 3

 

Rearranging the first, we have that  b = a + 3

 

But  b can' t equal a − 3  and  a + 3  at the same time !!!

 

So...I will assume that    b =   a − 3 

 

 

a^2 + (a-3)^2 = 15   expand

 

a^2 + a^2 −  6a + 9 =  15

 

2a^2 − 6a  −  6  = 0

 

a^2 − 3a − 3   = 0     the only solution to this that makes sense is that   a = [ 3 + √21 ] / 2  cm

 

And b =     a − 3  =   [ 3 + √21 ] / 2   − 3     =  [ − 3 + √21 ] / 2  cm

 

 

cool cool cool

 Dec 18, 2016
 #2
avatar+386 
0

Here are the solutions from the book:

 

One side is 9cm and the other 12cm.

 

 

 

Also, I think you forgot to square the hypotenuse when starting. That might be the problem...

TonyDrummer2  Dec 18, 2016
 #3
avatar+129852 
+5

Ah....I missed that......shame on me......let  me try again........!!!

 

a^2 + (a-3)^2 = 15^2   expand

 

a^2 + a^2 −  6a + 9 =  225   simplify

 

2a^2  − 6a  − 216  = 0   divide by 2  on both sides

 

a^2 −  3a − 108  = 0    factor

 

(a  − 12 ) ( a + 9)   = 0 

 

Set both factors to 0 and the only solution to this that makes sense is that   a = 12   cm

 

And     b =  a − 3   =  12 −  3   =  9 cm

 

 

 

cool cool cool

 Dec 18, 2016
 #4
avatar+386 
0

I get what you're doing but how can I put this into maths:

 

Set both factors to 0 and the only solution to this that makes sense is that   a = 12   cm

TonyDrummer2  Dec 18, 2016

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